T owards Realistic Stringy Models of Particle Physics & Cosmology as viewed by Gary Shiu University of Wisconsin
What is String Phenomenology?
Particle Physics & Cosmology • Deep connection, e.g., inflation, dark matter, neutrinos... • Both study the universe in the extreme conditions.
The Standard Model(s) Hierarchy problem Flatness, horizon, anisotropy SUSY? Inflation? Dark Energy? ..... .....
The Quiver Diagram
The Quiver Diagram Inflation, dark matter, ... Neutrinos, cosmic rays, ...
The Quiver Diagram CMB, graviational waves, ... . . . , y g r e n e k r a d , g n a b g i B
The Quiver Diagram C a l a b i - Y a S u U , G S Y 2 , , B . . r . a n e W o r l d , . . .
The Quiver Diagram String Phenomenology is the study of the links!
Are we ready for String Phenomenology?
The beginning of the unexpected ...
String Theory as a model of hadrons String theory began as a phenomenological model. Massless spin 2 particle: graviton!
Lessons • Ideas driven by phenomenological questions. • Need explicit models (c.f. QFT versus the Standard Model). • Fixing problems that plague the theory often leads to new and far-reaching ideas: ---Extra spin-2 particle graviton ---Tachyon SUSY • Works better than expected.
Meet the Quintuplets Type I IIA IIB HO HE
The Heterotic Supremacy • Type IIA/IIB: Difficult to implement non- Abelian gauge groups and chiral fermions. In fact, a no-go theorem for constructing the Standard Model. [Dixon, Kaplunovsky , Vafa] • Heterotic E8xE8: naturally contains GUTs (E6, SO(10), SU(5),...) and hidden sectors. • Type I and Heterotic SO(32): two other siblings that are largely ignored ...
String Phenomenology Begins
1985
Calabi-Yau Compactification N=1 SUSY Calabi-Yau Candelas, Horowitz, Strominger, Witten • Low energy physics (spectrum, couplings,...) determined by topology & geometry of M. • Building realistic heterotic string models: a huge industry beginning in the mid 80s.
The Score Card • E6, SO(10), SU(5) GUTs & MSSM-like vacua. • Rank . ≤ 22 • Constraints on gauge groups & matter reps. • Gauge unification. • Exotic matter: Schellekens’ theorem. Internal consistencies + phenomenological constraints a very tight system! However, two nagging problems ...
Moduli Problem Varying the size & shape of M In 4D, this freedom implies moduli: scalar fields φ i V ( φ i ) = 0 ∀ φ i
Moduli Problem Loss of predictivity • Different give inequivalent physics < φ i > (e.g., couplings, particle masses, ...) Phenomenological problems • Existence of light scalars: - Equivalence principle violations. - Time varying . α - Energy in can ruin cosmology. φ i
SUSY Breaking • Assumptions: - Non-perturbative effects (e.g., gaugino and/or ---- --matter condensate) break SUSY. - The same NP effects also lift all moduli. - SUSY scale ~ TeV (hierarchy problem). • But ... SUSY breaking effects on SM and moduli lifting potential not computed in a controlled stringy way.
1995
“When you come to a fork in the road, take it.” Yogi Berra
Return of the Lost Family HE HO Type IIB Type IIA Type I
The Post-1995 Picture heterotic on CY3 compactifications with flux Horava ! Witten intersecting branes M on G2 F on CY4 large extra dimensions Worth taking a fresh look at these long-standing problems.
All (new) roads lead to branes “Open string” “Closed string” “D-brane” Duality between geometry and branes: M-theory on G2, F-theory on CY4, Horava-Witten, ...
Brane World
Open Strings • Pioneering work (before 1995) Bianchi, Pradisi, Sagnotti, ... Polchinski .... • Recent review articles Formalism: Angelantonj, Sagnotti Model Building: Blumenhagen, Cvetic, Langacker, Shiu
Flux Compactification • Just like particle couples to gauge field via � A worldline • Dp-brane couples to p+1 index gauge fields: � A p +1 worldvolume • Thus p+2-form field strengths: F p +2 = dA p +1
Flux Compactification Various p ! cycles of M • For each p-cycle in M, we can turn on � Dirac Quantization F p ∈ Z Σ p • Analogous to turning on a B-field � � Energy ∼ 1 E 2 + B 2 � 8 π
Moduli Stabilization • The energy cost of a given flux depends on detailed geometry of M: V n 1 ,n 2 ,...,n k ( φ i ) � where n j = F , j = 1 , . . . , k. Σ j • Lift moduli ! φ i
Type IIB Flux Vacua • Superpotential induced by G 3 = F 3 − τH 3 � W = G ∧ Ω Gukov, Vafa, Witten M • Stabilizes the dilaton and complex structure moduli (shape) of M. Dasgupta, Rajesh, Sethi Greene, Schalm, Shiu Taylor, Vafa Giddings, Kachru, Polchinski ... • Additional mechanism stabilizes the Kahler Kachru, Kallosh, Linde, Trivedi moduli (size). ...
Flux Induced SUSY ISD G 3 D3
Flux Induced SUSY ISD G 3 D3 No soft terms
Flux Induced SUSY IASD G 3 D3
Flux Induced SUSY IASD G 3 D3 Non-trivial soft terms Explicit calculations. Lust, Reffert, Stieberger Camara, Ibanez, Uranga Grana, Grimm, Jockers, Louis
Can the Standard Model fit into this picture?
Chiral D-brane Models Two known ways to obtain chiral fermions: • Branes at singularities Calabi ! Yau D3 ! branes
• Intersecting branes U(N) (N,M) U(M) Type IIA Type IIB Type IIB Number of generations given by: [Π a ] ◦ [Π b ] = topological Π a Π b M
• Intersecting branes/magnetized D-branes “T oron” U(N) (N,M) U(M) Type IIA Type IIB Number of generations given by: [Π a ] ◦ [Π b ] = topological Π a Π b M
The Recipe • Pick your , and the associated sLAG Π a M • Chiral spectrum: Representation Multiplicity 1 2 ( π � a ◦ π a + π O6 ◦ π a ) a 1 2 ( π � a ◦ π a − π O6 ◦ π a ) a ( b ) a , π a ◦ π b ( b ) π � a , a ◦ π b • Tadpole cancellation (Gauss’s law): � N a (Π a + Π � a ) − 4Π O = 0 • K-theory constraints a
K-theory Constraints • D-brane charges are classified by K-theory. Minasian & Moore Witten • Discrete charges invisible in SUGRA, forbid certain non-BPS branes to decay. Sen • Uncanceled K-theory charges can manifest as Witten anomalies on D-brane probes. Uranga • Implications to the statistics of string vacua. Blumenhagen et al Schellekens et al • Direct construction of such discrete charged branes. Maiden, Shiu, Stefanski
T oward Realistic D-brane Models For a review, see, e.g., Blumenhagen, Cvetic, Langacker, Shiu, hep-th/0502005. • Many toroidal orbifold/orientifold models. • MSSM flux vacua. Marchesano, Shiu • D-branes in general Calabi-Yau (less is known about supersymmetric ). Π a • Gepner orientifolds Angelantonj, Bianchi, Pradisi, Sagnotti, Stanev Dijkstra, Huiszoon, Schellekens Blumenhagen, Weigard
How about Cosmology?
Inflation as a probe of stringy physics WMAP • Almost scale invariant, Gaussian primordial spectrum predicted by inflation is in good agreement with data. • A tantalizing upper bound on the energy density during inflation: V ∼ M 4 GUT ∼ (10 16 GeV) 4 H ∼ 10 14 GeV i.e.,
Planckian Microscope? ∆ C � P 1 / 2 ( k ) C � 0.00011 0.012 0.01 0.000109 0.008 0.006 0.000108 0.004 0.002 0.000107 0 1. 10. 100. 1000. 10000. 100000. 6 -0.002 10 0 200 400 600 800 1000 1200 1400 k � Easther, Greene, Kinney, Shiu Schalm, Shiu, van der Schaar
Brane Inflation Dvali and Tye Extra Extra Our Anti ! Brane Brane Brane
Brane Inflation Dvali and Tye Extra Extra Our Anti ! Brane Brane Brane
Brane Inflation Stringy signatures, e.g., gravitational waves ... radiation Our + D strings Brane + F strings Tye et al Copeland, Myers, Polchinski ...
Brane Inflation Are the branes moving slowly enough? Is reheating efficient? Can the cosmic strings be stable? Warping by Fluxes
Warped Throats • Fluxes back-react on the metric: AdS 5 IR UV e.g., Klebanov, Strassler “warped deformed conifold”
Warped Throats 1 γ = � 1 − f ( φ ) ˙ φ 2 D3 D3 DBI inflation Silverstein and Tong � � � � d 4 x √− g 1 − f ( φ ) ˙ f ( φ ) − 1 φ 2 − V ( φ ) − f ( φ ) − 1 S = − φ 2 ≤ f ( φ ) − 1 ˙ Casual speed limit: warp factor
Warped Throats • Cosmic strings spatially separated from SM branes: not susceptible to breakage. • Reheating via tunneling is efficient due to KK versus graviton wavefunctions. Barneby, Burgess, Cline Kofman and Yi Chialva, Shiu, Underwood Frey, Mazumdar, Myers
Non-Gaussianities Large 3-point correlations that are potentially observable. Moreover, distinctive shape. [Figures from Chen, Huang, Kachru, Shiu] − 54 < f NL < 114 (WMAP3) f NL ∼ 5 (PLANCK) 3 0.2 2 0.8 0.8 0.1 1 0.6 0 0 0.6 0.2 0.2 0.4 0.2 0.2 0.4 0.4 0.4 0.4 0.4 0.2 0.6 0.6 0.2 0.6 0.6 0.8 0.8 0.8 0.8 ( f NL ∼ γ 2 ) Slow-roll DBI ( f NL ∼ � )
Have we gone too far?
The Landscape How many string vacua are there?
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